Reflexive subspaces of some Orlicz spaces

• Autorzy: Emmanuelle Lavergne
• Języki publikacji: EN

Abstrakty

EN

We show that when the conjugate of an Orlicz function ϕ satisfies the growth condition Δ⁰, then the reflexive subspaces of $L^ϕ$ are closed in the L¹-norm. For that purpose, we use (and give a new proof of) a result of J. Alexopoulos saying that weakly compact subsets of such $L^ϕ$ have equi-absolutely continuous norm.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 113
• Numer: 2
• Strony: 333-340

Daty

wydano

2008

Twórcy

autor

Emmanuelle Lavergne

• Laboratoire de Mathématiques Lens (LML), Équipe d'Accueil EA 2462, Fédération CNRS Nord-Pas-de-Calais FR 2956, Faculté des Sciences Jean Perrin, Université d'Artois, rue Jean Souvraz S.P. 18, 62307 Lens Cedex, France

Identyfikatory

DOI

10.4064/cm113-2-13